137edo: Difference between revisions
+one-linear overview and note more 5-limit commas |
→Regular temperament properties: update |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| -217 137 }} | ||
| {{ | | {{Mapping| 137 217 }} | ||
| 0.3865 | | +0.3865 | ||
| 0.3866 | | 0.3866 | ||
| 4.41 | | 4.41 | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| -21 3 7 }}, {{monzo| -13 17 -6 }} | ||
| {{ | | {{Mapping| 137 217 318 }} | ||
| 0.3887 | | +0.3887 | ||
| 0.3157 | | 0.3157 | ||
| 3.60 | | 3.60 | ||
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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| 3\137 | | 3\137 | ||
| 26.28 | | 26.28 | ||
| | | 49/48 | ||
| [[Sfourth]] ( | | [[Sfourth]] (137d…) | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 68: | Line 70: | ||
| 315.33 | | 315.33 | ||
| 6/5 | | 6/5 | ||
| [[Parakleismic]] | | [[Parakleismic]] (137d) / [[counterpara]] (137) | ||
|- | |||
| 1 | |||
| 53\137 | |||
| 464.23 | |||
| 72/55 | |||
| [[Borwell]] | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 82: | Line 90: | ||
| [[Emka]] (137d) / [[emkay]] (137) | | [[Emka]] (137d) / [[emkay]] (137) | ||
|} | |} | ||
<nowiki>* | <nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | ||
== Diagrams == | == Diagrams == | ||